SCHAUM_S_MATHEMATICAL_HANDB.PDF

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The pur-pose of this handbook is to supply a collection of mathematical formulas and
tables which will prove to be valuable to students and research workers in the fields of
mathematics, physics, engineering and other sciences. TO accomplish this, tare has been
taken to include those formulas and tables which are most likely to be needed in practice
rather than highly specialized results which are rarely used. Every effort has been made
to present results concisely as well as precisely SOthat they may be referred to with a maxi-
mum of ease as well as confidence.
Topics covered range from elementary to advanced. Elementary topics include those
from algebra, geometry, trigonometry, analytic geometry and calculus. Advanced topics
include those from differential equations, vector analysis, Fourier series, gamma and beta
functions, Bessel and Legendre functions, Fourier and Laplace transforms, elliptic functions
and various other special functions of importance. This wide coverage of topics has been
adopted SOas to provide within a single volume most of the important mathematical results
needed by the student or research worker regardless of his particular field of interest or
level of attainment.
The book is divided into two main parts. Part 1 presents mathematical formulas
together with other material, such as definitions, theorems, graphs, diagrams, etc., essential
for proper understanding and application of the formulas. Included in this first part are
extensive tables of integrals and Laplace transforms which should be extremely useful to
the student and research worker. Part II presents numerical tables such as the values of
elementary functions (trigonometric, logarithmic, exponential, hyperbolic, etc.) as well as
advanced functions (Bessel, Legendre, elliptic, etc.). In order to eliminate confusion,
especially to the beginner in mathematics, the numerical tables for each function are sep-
arated, Thus, for example, the sine and cosine functions for angles in degrees and minutes
are given in separate tables rather than in one table SOthat there is no need to be concerned
about the possibility of errer due to looking in the wrong column or row.
1 wish to thank the various authors and publishers who gave me permission to adapt
data from their books for use in several tables of this handbook. Appropriate references
to such sources are given next to the corresponding tables. In particular 1 am indebted to
the Literary Executor of the late Sir Ronald A. Fisher, F.R.S., to Dr. Frank Yates, F.R.S.,
and to Oliver and Boyd Ltd., Edinburgh, for permission to use data from Table III of their
book
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also wish to express my gratitude to Nicola Menti, Henry Hayden and Jack Margolin
for their excellent editorial cooperation.
M. R. SPIEGEL
Rensselaer Polytechnic Institute
September, 1968
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CONTENTS
Page
1.
Special
Constants..
.............................................................
1
2
2.
Special Products and Factors
....................................................
3.
The Binomial Formula and Binomial Coefficients
.................................
4.
Geometric Formulas ............................................................
5.
Trigonometric Functions
........................................................
6.
Complex Numbers ...............................................................
7.
Exponential and Logarithmic Functions
.........................................
8.
Hyperbolic Functions ...........................................................
9.
Solutions of Algebraic Equations
................................................
10.
Formulas from Plane Analytic Geometry
........................................
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
2s.
26.
27.
28.
29.
30.
3
5
11
21
23
26
32
34
40
46
53
57
94
..10 1
..lO 3
.104
Special
Plane
Curves........~
...................................................
Formulas from Solid Analytic Geometry ........................................
Derivatives .....................................................................
Indefinite Integrals ..............................................................
Definite Integrals ................................................................
The
Gamma
Function .........................................................
The Beta Function ............................................................
Basic Differential Equations and Solutions
.....................................
Series of Constants..............................................................lO
Taylor Series...................................................................ll
Bernoulliand
Euler Numbers .................................................
.............................................
Formulas from Vector Analysis..
Bessel Functions..
7
0
..114
..116
..~3 1
..13 6
6
.149
Fourier Series ................................................................
............................................................
Legendre Functions.............................................................l4
Associated Legendre Functions
.................................................
Hermite Polynomials............................................................l5
Laguerre Polynomials ..........................................................
Associated Laguerre Polynomials
................................................
Chebyshev Polynomials..........................................................l5
1
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